ArticleOriginal scientific text
Title
On the disc-convexity of complex Banach manifolds
Authors 1, 1
Affiliations
- Department of Mathematics, Institute of Pedagogy of Hanoi 1, Cau giay, Tu liem, Ha noi, Vietnam
Abstract
The Banach hyperbolicity and disc-convexity of complex Banach manifolds and their relations are investigated.
Keywords
Banach manifold, hyperbolic, disc-convex
Bibliography
- R. Brody, Compact manifolds and hyperbolicity, Trans. Amer. Math. Soc. 235 (1978), 213-219.
- K. Diederich and N. Sibony, Strange complex structures on Euclidean space, J. Reine Angew. Math. 311/312 (1979), 397-407.
- G. Fischer, Complex Analytic Geometry, Lecture Notes in Math. 538, Springer, 1976.
- A. Hirschowitz, Pseudoconvexité au-dessus d'espaces plus ou moins homogènes, Invent. Math. 26 (1974), 303-322.
- S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Dekker, 1970.
- S. Kobayashi, Intrinsic distances, measures and geometric function theory, Bull. Amer. Math. Soc. 82 (1976), 357-416.
- S. Lang, Introduction to Complex Hyperbolic Spaces, Springer, 1987.
- P. Mazet, Analytic Sets in Locally Convex Spaces, North-Holland Math. Stud. 121, North-Holland, 1987.
- J. P. Ramis, Sous-ensembles Analytiques d'une Variété Banachique Complexe, Ergeb. Math. Grenzgeb. 53, Springer, 1970.
- B. Shabat, Introduction to Complex Analysis, Part II, Functions of Several Variables, Transl. Math. Monographs 110, Amer. Math. Soc., 1992.
- B. Shiffman, Extension of holomorphic maps into hermitian manifolds, Math. Ann. 194 (1971), 249-258.
- N. Sibony, Prolongement des fonctions holomorphes bornées et métrique de Carathéodory, Invent. Math. 29 (1975), 205-230.
- B. D. Tac, Extending holomorphic maps in infinite dimensions, Ann. Polon. Math. 54 (1991), 241-253.
- D. D. Thai, Royden-Kobayashi pseudometric and tautness of normalizations of complex spaces, Boll. Un. Mat. Ital. A (7) 5 (1991), 147-156.
- H. Toruńczyk, Smooth partitions of unity on some non-separable Banach spaces, Studia Math. 66 (1973), 44-51.
- T. Urata, The hyperbolicity of complex analytic spaces, Bull. Aichi Univ. of Education 31 (1982), 65-75.
- E. Vesentini, Invariant distances and invariant differential metrics in locally convex spaces, in: Spectral Theory, Banach Center Publ. 8, PWN-Polish Sci. Publ., Warszawa, 1982, 493-512.
- M. Zaĭdenberg, The Picard theorem and hyperbolicity, Siberian Math. J. 24 (1983), 858-867 (English transl.).
- M. Zaĭdenberg, S. Kreĭn, P. Kuchment and A. Pankov, Banach bundles and linear operators, Uspekhi Mat. Nauk 30 (1975), no. 5, 101-157 (in Russian).